The Piececlopedia is intended as a scholarly reference concerning the history and naming conventions of pieces used in Chess variants. But it is not a set of standards concerning what you must call pieces in newly invented games.

Piececlopedia: Griffon

Historical Notes

The original use of the Griffon is in the game Grande Acedrex. This game is
described in Libro del Acedrex, a game book that dates from
1283 under Spanish King Alphonso the Tenth.

John Williams-Brown uses the piece in his Meta-Chess book, although he uses a
slightly more limited version (see below). He also suggests the name
Hippogriff (described below) for a historical piece similar to the
Griffon which was called the Giraffe.

For his game RennChess Eric
Greenwood invented a more powerful piece called the Cavalier which is
derived from the Griffon.

Note that in the English language, Griffin and Gryphon are also
accepted spellings for Griffon.

Movement

The Griffon moves one square diagonally in any direction, the
continues away from the starting square in an orthogonal direction.
Its path must be unoccupied; it can not jump over pieces. It captures
an enemy piece by moving onto the square occupied by that piece.

According to Pritchard, Gollon, Chessvariants, and Betza the Griffon can
end its move on a diagonally adjacent square. The version used by
Williams-Brown does not allow this - the Griffon passes over
diagonally adjacent square, which much be unoccupied, and can only
stop on subsequent orthogonally adjacent squares.

Movement Diagram

In the diagram below, the griffon can move to any of the squares
marked by a red circle. The griffon could also capture any piece that
occupied one of these squares.

Remarks

In general, the Griffon is a powerful piece that is more effective in
the endgame where it has more open space to move. Williams-Brown
notes that the Griffon has asymmetrical-retreat properties; in
other words, when a Griffon moves from point A to point B, a
subsequent move from point B back to point A will inevitably be along
a different path, which may be blocked. On a crowded board the
Griffon may be easily trapped.

In the diagram below, white has just moved his Griffon from b1 to a6.
But the path back from a6 to b1, or any other safe square, is blocked
by the black pawn on b5. If black plays Rf6, the best white can get
for his Griffon is the Pawn, and black wins the game.

A Griffon and a King can force checkmate a lone King, although the
procedure requires some thought. After the lone King is forced to the
side of the board, the Griffon must make a 'waiting' move - similar to
the one made by the Rook in a K and R vs. K endgame - so that his King
can get opposition to the lone King. A slight difficulty arises in
the fact that the Griffon must always move to a different file or
rank. If a Griffon has the lone king trapped on the first rank for
example, the Griffon must make a waiting move by moving from the first
rank to the third, or vice-versa.

The Hippogriff

The Hippogriff originally appeared in the historical game Tamerlane Chess, where it
was called the Giraffe. Giraffe, however, is
already commonly used for another piece; John Williams-Brown suggested
the name Hippogriff. The Hippogriff moves the same way as the
Griffon, except that it must move at least three squares orthogonally
after the initial diagonal move. (The Hippogriff is in fact similar
to the Giraffe in that the closest squares it can move to are the same
as those that the Giraffe would move to; the Hippogriff can almost be
thought of as a combination of the Giraffe and Griffon, although it
does not leap other pieces like the Giraffe does.)

In the diagram below, the Hippogriff can move to any of the squares
marked by a large red circle, but not to any of the squares marked by
a small red circle. The small-circled square must be unoccupied or
the else the pieces on those squares - friendly or enemy - will block
the path of the Hippogriff in that direction.

The Hippogriff is a much weaker and more awkward piece than the
Griffon. Note, for example, that a Griffon on an 8x8 board can move
to more squares than a Hippogriff on a 12x12 board, and requires at
least three moves to get to a diagonally adjacent square. On an 8x8
board, the shortest path for a Hippogriffon to get from a1-b2 is by
the route a1-b5-f6-g1-b2 .

Comments

The Hippogriff of Tamerlane Chess is explained on the same Griffon page of Jeremy Good. Hippogriff moves like earlier Gryphon/Griffon/(different spellings), but is excluded from the nearby squares, that is those within the 7x7 square perimeter. Since also blockable, Hippogriff is subset of Gryphon.

1283 was year of publication of Grande Acedrez with first use of Gryphon. Timur Lenk, inventor of namesake Timur's or Tamerlane Chess (1336-1405) has Giraffe as Hippogriff, the classic Gryphon that is excluded from those near squares. So there was a hundred years to ponder better implementation of Gryphon into Hippogriff. We can presume intellectual transfer of ideas from Spain to Persia, just as there was trade continually between Inuit Arctic and Siberia.
https://www.google.com/search?sa=G&hl=en&q=gustave+dor%C3%A9&tbm=isch&tbs=simg:CAQSlQEJJONZ7scbvBUaiQELEKjU2AQaAggCDAsQsIynCBpiCmAIAxIo_1BHoEb4XzAv7EbIcuhbGD7kLkwy5OrU62D7XPr46uDr8Ldks_1y20Ohow8XOAb2THltHscfBShsKNZ48M1-z-jR2xsQ0CbEuLXPHMIVWT14Wi0srN9dfMhUs3IAQMCxCOrv4IGgoKCAgBEgQPwcxyDA,isz:l&ved=0ahUKEwi_5f-G2pzQAhXoyFQKHRL7APsQ2A4IHigE&biw=1920&bih=974#imgrc=Ackhrp7O_-BASM%3A

I was talking about a gryphon on b1, not a6. From b1, it can move diagonally to c2, then continue straight upward to c5. Note that no pieces obstruct this movement. Also, according to the description, black's king would have to have been on c5 when the gryphon was on b1.

In the 6x6-board demonstration of the gryphon's move, an impossible situation is shown. A gryphon at b1 checks the king at c5 (and - irrelevantly- attacks the rook on g2). If the black king is in check on white's move, white can simply take the black king! This is illegal, and implies that the black king either moved into check or refused to move out of it(both of which are illegal).